There was a recent question: Name of black keys as a starting point in a musical series. Several others and I answered it. In my answer, I said:
"E♭ will require 3 flats. D♯ would require double sharps."
I used the phrase, "would require double sharps" to avoid giving a specific number of sharps.
So, if asked: How many sharps in D♯ major? What would you say?
a) 9 sharps.
b) 5 sharps and 2 double sharps.
c) 7 sharps, 2 of which are double.
d) It's a silly question, no one would use that key.
e) Something else.
f) There is no good answer to this question.
The first is mathematically attractive. If you pick a pair of enharmonic keys X sharp and (X + 1) flat then the number of sharps in one plus the number of flats in the other would always be 12. However, I am not suggesting that this should be taken as a justification of this answer.
I am not suggesting that this is an important question. It is just a curiosity inspired by the question that I referred to. If there is no good answer then that is the answer. I have added that option though d) could be regarded as covering that one.